Overview:
Raw data from any series of measurements, such as test scores, heights, or sales figures, usually needs to be organized in some way before it can be used. One of the ways that data can be organized is in a frequency distribution. Then the range of data can be determined and other measurements of the data can be made.
What Is the Range?
The range of data is the difference between the highest and lowest values. In a previous experiment, the heights of 20 randomly-selected 12 year olds were measured, so that the following values were obtained: 43 48 55 55 56 57 59 60 60 60 61 61 63 64 64 65 67 68 70 72. They are arranged in order between the shortest and the tallest, so it is easier to see the range, from 72-43, a difference of 29 inches.
What Is the Median?
The median of a set of data is that value that divides the set of data in half. In the above distribution, the median would be a score that would have half the values below it and half the values above it. The median would be halfway between the 10th and the 11th score. Since the 10th score is 60 and the 11th score is 60, for all practical purposes the median would be 60.
What Are Quartiles?
When the median of a set of data is calculated, it divides the scores into an upper half and a lower half, also called an upper quartile and a lower quartile. The medians of those smaller sets of data can be calculated. Using the height data for an example, the median of the lower quartile would be halfway between the fifth and sixth score or (56 + 57)/2 = 56.5. The median for the upper quartile would be halfway between the 15th and 16th scores or (64 + 65)/2 = 64.5. The interquartile range is the difference between the median of the upper quartile and lower quartile or 64.5 – 56.5 = 8 inches.
What Is a Box and Whisker Plot?
A box and whisker plot uses a number line that extends a little beyond the range for the data. In this example, a number line could be chosen that would go from 40 to 80. Next, the extreme values of 43 and 72 would be plotted, then the median of 60, then the median of the lower quartile, 56.5 and the upper quartile 64.5. A box could be drawn between 56.5 and 64.5 and lines (the ‘whiskers’) from the box to the lower value of 43 and the upper value of 72.
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